Results 11 to 20 of about 10,834,928 (363)
Differentiability of the arithmetic volume function [PDF]
Journal of the London Mathematical Society, 2008 We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle ...
Chen, Huayi
core +6 more sources
The arithmetic derivative and Leibniz-additive functions [PDF]
Annales Mathematicae et Informaticae, 2018 An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$ f(mn)=f(m)h_f(n)+f(n)h_f(m) $$ for all positive ...
Haukkanen, Pentti +2 more
core +5 more sources
Function Interval Arithmetic [PDF]
International Congress on Mathematical Software, 2014 We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1 ...
Duracz, Jan +3 more
openaire +4 more sources
Frontal Midline Theta Oscillations during Mental Arithmetic: Effects of Stress
Frontiers in Behavioral Neuroscience, 2015 Complex cognitive tasks such as mental arithmetic heavily rely on intact, well-coordinated prefrontal cortex (PFC) function. Converging evidence suggests that frontal midline theta (FMT) oscillations play an important role during the execution of such ...
Matti eGärtner +5 more
doaj +2 more sources
Arithmetic of quantum entropy function [PDF]
Journal of High Energy Physics, 2009 LaTeX file, 27 pages; v2: minor ...
A. Sen
openaire +5 more sources
Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models [PDF]
Neural Information Processing Systems, 2023 Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while ...
Guillermo Ortiz-Jiménez +2 more
semanticscholar +1 more source
Teaching Arithmetic to Small Transformers [PDF]
arXiv.org, 2023 Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee +4 more
semanticscholar +1 more source
Grokking modular arithmetic [PDF]
arXiv.org, 2023 We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various modular ...
A. Gromov
semanticscholar +1 more source
International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary In this contribution, we propose a detailed study of interpolation‐based data‐driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, that is, we analyze frequency‐response data.
Quirin Aumann, Ion Victor Gosea
wiley +1 more source